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arXiv:cs/0508094 · IEEE International Symposium on Information Theory (ISIT)

Conference key agreement and quantum sharing of classical secrets with noisy GHZ states

Kai Chen, Hoi-Kwong Lo

Published Jan 1, 2005• 10 citations
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Abstract

We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then consider the applications of our distillation schemes for two cryptographic tasks - namely, (a) conference key agreement and (b) quantum sharing of classical secrets. In particular, we construct "prepare-and-measure" protocols. Also we study the yield of those protocols and the threshold value of the fidelity above which the protocols can function securely. Surprisingly, our protocols function securely even when the initial state does not violate the standard Bell-inequalities for GHZ states. Experimental realization involving only bipartite entanglement is also suggested

DOI
10.1109/isit.2005.1523616

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We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then consider the applications of our distillation schemes for two cryptographic tasks - namely, (a) conference key agreement and (b) quantum sharing of classical secrets. In particular, we construct "prepare-and-measure" protocols. Also we study the yield of those protocols and the threshold value of the fidelity above which the protocols can function securely. Surprisingly, our protocols function securely even when the initial state does not violate the standard Bell-inequalities for GHZ states. Experimental realization involving only bipartite entanglement is also suggested
Abstract — We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then consider the applications of our distillation schemes for two cryptographic tasks—namely, (a) conference key agreement and (b) quantum sharing of classical secrets. In particular, we construct “prepare-and-measure ” protocols. Also we study the yield of those protocols and the threshold value of the fidelity above which the protocols can function securely. Surprisingly, our protocols will function securely even when the initial state does not violate the standard Bell-inequalities for GHZ states. Experimental realization involving only bi-partite entanglement is also suggested. I.
We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then apply our distillation schemes to the tri-partite case for three cryptographic tasks---namely, (a) conference key agreement, (b) quantum sharing of classical secrets and (c) third-man cryptography. Moreover, we construct ``prepare-and-measure'' protocols for the above three cryptographic tasks which can be implemented with the generation of only a single entangled pair at a time. This gives significant simplification over previous experimental implementations which require two entangled pairs generated simultaneously. We also study the yields of those protocols and the threshold values of the fidelity above which the protocols can function securely. Rather surprisingly, our protocols will function securely even when the initial state does not violate the standard Bell-inequalities for GHZ states.
Quantum conference key agreement (QCKA) protocols utilize GHZ states to establish shared group keys between multiple parties. While previous work has shown that standard Classical Advantage Distillation (CAD) protocols can sometimes benefit QCKA performance, it was unknown if past results were asymptotically tight. In this work, we design a new CAD protocol, "Selective Classical Advantage Distillation (S-CAD)", for QCKA, which generalizes prior QCKA+CAD work and allows the parties to selectively enable or disable CAD. We derive an asymptotic proof of security against general coherent attacks, which outperforms prior work. Finally, we evaluate in a variety of simulated star network topologies, showing when S-CAD can help, and when it is best to disable CAD entirely.
We approach two interconnected problems of quantum information processing in networks: Conference key agreement and entanglement distillation, both in the so-called source model where the given resource is a multipartite quantum state and the players interact over public classical channels to generate the desired correlation. The first problem is the distillation of a conference key when the source state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of local operations and classical communication (LOCC) from the given mixed state. These problem settings extend our previous paper [IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive novel lower bounds on the distillable conference key from any multipartite quantum state by means of non-interacting communication protocols. Secondly, we establish novel lower bounds on the yield of GHZ states from multipartite mixed states. Namely, we present two methods to produce bipartite entanglement between sufficiently many nodes so as to produce GHZ states. Next, we show that the conference key agreement protocol can be made coherent under certain conditions, enabling the direct generation of multipartite GHZ states.
We investigate the task of conference key agreement in near-term quantum networks, where the nodes are connected by sources of bipartite entangled states, under the class of local operations not requiring quantum memory. We derive upper bounds on the distillable conference key depending on the network topology and degree of entanglement of the sources, and prove tightness of these bounds for some particular cases. In these cases, we show that pairwise bipartite key distillation followed by merging the bipartite keys into the conference key is optimal.